Prove the following: If (p) is prime, then (phileft(p^{i}ight)=p^{i}-p^{i-1}). Hint: What numbers have a factor in common

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Prove the following: If \(p\) is prime, then \(\phi\left(p^{i}ight)=p^{i}-p^{i-1}\). Hint: What numbers have a factor in common with \(p^{i}\) ?

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